# Prime Factorization

Prime factorization is a fundamental concept in number theory, essential for understanding the unique composition of natural numbers. It involves breaking down a given integer into its smallest prime factors, providing insight into the building blocks of mathematical structures. Through prime factorization, complex numbers can be simplified, and relationships between different integers can be revealed. This process forms the basis for various mathematical algorithms and is crucial in fields such as cryptography, computer science, and abstract algebra. Understanding prime factorization is not only valuable for solving mathematical problems but also for appreciating the intricate beauty of number theory.

- Which of the following numbers has the largest number of unique prime factors?: {573, 951, 825, 639}
- How do you write the prime factorization of #-120r^2st^3#?
- How can you use prime factorization to determine if 856 is evenly divisible by 7?
- Which numbers in the following set are prime numbers: (4,7,31, 117, 324)?
- How do you find all factors of 45?
- Is 53 prime or composite?
- What are the prime factors of 102?
- Which of the following numbers has the largest number of unique prime factors?: {78, 217, 74, 420}
- How do you write the prime factorization of #21gh^3#?
- How do you write the prime factorization of 96?
- How do you write 720 as a product of its prime factors?
- How do you write the prime factorization of #64n^3#?
- How do you use prime factorization to find the least common multiple of 75 and 45?
- How do you use prime factorization?
- How do you find the prime factorization of 20?
- What is the prime factorization of 125?
- How do you express 3080 as a product of prime factors?
- How do you write 18 as a product of prime factors?
- How many prime factors does 120 have?
- How do you write the prime factorization of #-25z^3#?